Intrasubband and intersubband transitions in lightly and heavily doped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ multiple quantum wells

We use a polarizer to investigate quantum-well infrared absorption, and report experimental results as follows. The intrasubband transition was observed in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ multiple quantum wells (MQWs) when the incident infrared radiation (IR) is polarized parallel to the MQW plane. According to the selection rule, an intrasubband transition is forbidden. Up to now, most studies have only observed the intersubband transition between two states with opposite parity. However, our experiment shows not only the intersubband transitions, but also the intrasubband transitions. In our study, we also found that for light doping in the well $(4\mathrm{}\times {10}^{18}{\mathrm{cm}}^{\mathrm{-}3}),$ the intrasubband transition occurs only in the lowest subband, while for the heavy doping $(8\mathrm{}\times {10}^{18}{\mathrm{cm}}^{\mathrm{-}3}),$ such a transition occurs not only in the lowest subband, but also in the first excited one, because of the electron subband filling. Further experimental results show a linear dependence of the intrasubband transition frequency on the root of the well doping density. These data are in good agreement with our numerical results. Thus we strongly suggest that such a transition can be attributed to plasma oscillation. Conversely, when the incident IR is polarized perpendicular to the MQW plane, intersubband-transition-induced signals appear, while the intrasubband-transition-induced spectra disappear for both light and heavy well dopings. A depolarization blueshift was also taken into account to evaluate the intersubband transition spectra at different well dopings. Furthermore, we performed a deep-level transient spectroscopy (DLTS) measurement to determine the subband energies at different well dopings. A good agreement between DLTS, infrared absorption, and numerical calculation was obtained. In our experiment, two important phenomena are noteworthy: (1) The polarized absorbance is one order of magnitude higher than the unpolarized spectra. This puzzling result is well explained in detail. (2) When the IR, polarized perpendicular to the well plane, normally irradiates the 45°-beveled edge of the samples, we only observed intersubband transition spectra. However, the intrasubband transition signals caused by the in-plane electric-field component are significantly absent. The reason is that such in-plane electric-field components can cancel each other out everywhere during the light propagating in the samples. The spectral widths of bound-to-bound and bound-to-continuum transitions were also discussed, and quantitatively compared to the relaxation time τ, which is deduced from the electron mobility. The relaxation times deduced from spectral widths of bound-to-bound and bound-to-continuum transitions are also discussed, and quantitatively compared to the relaxation time deduced from electron mobility.